Problem: The measures of the four interior angles of a quadrilateral are $x, 2x, x + 20$ and $x + 40$ degrees. How many degrees are in the measure of the smallest interior angle of the quadrilateral?
Answer: The sum of the angles of a quadrilateral is $360^\circ$, so \[x + 2x + (x+20) + (x+40) = 360.\] Simplifying the left side gives $5x + 60 = 360$, so $5x = 300$ and $x=60$. Therefore, the angles of the quadrilateral are $60^\circ$, $120^\circ$, $80^\circ$, and $100^\circ$, which means that the smallest is $\boxed{60^\circ}$.